Modelos de ocupación

class: center, middle, inverse, title-slide

.title[
# Modelos de ocupación
]
.subtitle[
## Uniandes, 2023
]
.author[
### Diego J. Lizcano, Ph.D. test
]
.institute[
### SCMAS, Destino Naturaleza (USAID)
]
.date[
### 2023-05-05
]

---

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# Modelos de ocupación

## Uniandes, 2023

### Diego J. Lizcano, Ph.D. test

???

Welcome to the webinar on sharing on short notice

Where we'll show you how to get your teaching materials online with R Markdown.

---
class: center, middle

# Gracias a

## Aída Otálora-Ardila
![:scale 40%](data:image/png;base64,#img/Aida_Otalora_Ardila.jpg)

---
class: inverse, center, middle

# Get Started

---
class: inverse, center

# Diego J. Lizcano

[<svg aria-hidden="true" role="img" viewBox="0 0 496 512" style="height:1em;width:0.97em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:black;overflow:visible;position:relative;"><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>](https://github.com/dlizcano) [<svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:black;overflow:visible;position:relative;"><path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"/></svg>](https://twitter.com/dlizcano)   [<svg aria-hidden="true" role="img" viewBox="0 0 640 512" style="height:1em;width:1.25em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:black;overflow:visible;position:relative;"><path d="M579.8 267.7c56.5-56.5 56.5-148 0-204.5c-50-50-128.8-56.5-186.3-15.4l-1.6 1.1c-14.4 10.3-17.7 30.3-7.4 44.6s30.3 17.7 44.6 7.4l1.6-1.1c32.1-22.9 76-19.3 103.8 8.6c31.5 31.5 31.5 82.5 0 114L422.3 334.8c-31.5 31.5-82.5 31.5-114 0c-27.9-27.9-31.5-71.8-8.6-103.8l1.1-1.6c10.3-14.4 6.9-34.4-7.4-44.6s-34.4-6.9-44.6 7.4l-1.1 1.6C206.5 251.2 213 330 263 380c56.5 56.5 148 56.5 204.5 0L579.8 267.7zM60.2 244.3c-56.5 56.5-56.5 148 0 204.5c50 50 128.8 56.5 186.3 15.4l1.6-1.1c14.4-10.3 17.7-30.3 7.4-44.6s-30.3-17.7-44.6-7.4l-1.6 1.1c-32.1 22.9-76 19.3-103.8-8.6C74 372 74 321 105.5 289.5L217.7 177.2c31.5-31.5 82.5-31.5 114 0c27.9 27.9 31.5 71.8 8.6 103.9l-1.1 1.6c-10.3 14.4-6.9 34.4 7.4 44.6s34.4 6.9 44.6-7.4l1.1-1.6C433.5 260.8 427 182 377 132c-56.5-56.5-148-56.5-204.5 0L60.2 244.3z"/></svg>](https://dlizcano.github.io)

![:scale 40%](data:image/png;base64,#img/7D2_5770-2.jpg)

Biólogo. Universidad de los Andes, Bogotá-Colombia.

Ph.D. University of Kent, Canterbury, UK.  
  
Ecology and conservation of large mammals (Andes).

---

# En este mini taller...

Vamos a usar
![:scale 20%](data:image/png;base64,#https://www.r-project.org/logo/Rlogo.png)

Y muy recomendado usar ![:scale 30%](data:image/png;base64,#https://www.rstudio.com/wp-content/uploads/2018/10/RStudio-Logo-Flat.png)

![:scale 40%](data:image/png;base64,#https://media.giphy.com/media/xmYbQrxezZkmk/giphy-downsized.gif)

---
class: center, top, inverse

# Ecology
### Charles Krebs
![:scale 50%](data:image/png;base64,#https://www.zoology.ubc.ca/~krebs/images/charley_cleth.jpg)

---

# Ecology: Study of interactions that determine **Distribution and Abundance**

.left-column[
![](data:image/png;base64,#img/ecology.jpg)
]

.right-column[
### Distribution:

Where are they.

### Abundance:

How many?.

]

Related to the problem of counting organisms!

---

# Contar animales no es un problema trivial...

![](data:image/png;base64,#https://media.giphy.com/media/11aqMcSy5tsgow/giphy.gif)

Los animales se mueven

---

name: surprise
class: right, middle
background-image: url(data:image/png;base64,#https://media.giphy.com/media/5zoxhCaYbdVHoJkmpf/giphy.gif)
background-size: contain
background-position: left

.pull-right[
### Como contar animales: Un problema muy antiguo en Ecología
]

---

### Como Ecologo: El mapa de nuestros sueños

![Mapa de densidad](data:image/png;base64,#img/kanguro.png)

#### at some point, we had to count the kangaroos

---

# Contar Animales

![Obtener densidad](data:image/png;base64,#img/pinguinos.jpg)

#### Fácil para animales que son llamativos y que se agrupan.

---

# Contar Animales

![Obtener densidad](data:image/png;base64,#img/432.jpg)
#### No es tan fácil si no se agrupan. Capturar - Marcar - Recuperar. Distancia

---

# Contar Animales

![Obtener densidad](data:image/png;base64,#img/Moose-capture_011.jpg)

#### Para algunas especies es engorroso, poco práctico y muy costoso

---

### Abundancia Relativa

![:scale 80%](data:image/png;base64,#img/bird_abundance.jpg)

#### Una variable indicadora del estado de la población

No sé cuántos hay, pero sí sé dónde hay más y dónde hay menos.

---

# Sin embargo...

![:scale 80%](data:image/png;base64,#http://i.giphy.com/nejXhE8hnCiQ0.gif)
#### Los animales se mueven y se esconden (camuflaje)

---
class: center
# El muestreo no es infalible

![:scale 120%](data:image/png;base64,#https://i.giphy.com/media/piPn7Cv4KmlVbOSa5c/giphy.webp)

Los biólogos no somos superhéroes. ¡Cometemos errores!

#### Concepto de detectabilidad y detección imperfecta

---

# La detectabilidad depende de

## 1. Condiciones de muestreo (clima, tiempo).

## 2. La capacidad del observador (sensor).

## 3. 3. La biología de la especie que se está muestreando.

### Este error debe ser considerado cuidadosamente para evitar sesgos en las estimaciones de abundancia.

---

# Cómo se produce el error de detección (Guillera‐Arroita 2016)

see ppt ![:scale 60%](data:image/png;base64,#img/detection.png)

##### ¡¡¡Es un error importante que debe ser considerado en el diseño muestral!!!

[por que considerarlo?](https://gguilleraresearch.wordpress.com/2017/02/28/accounting-for-imperfect-detection-in-the-modelling-of-species-distributions-range-dynamics-and-communities/)

---

# Mackenzie et al 2002, 2003 al rescate...

![](data:image/png;base64,#img/mackenzie.png)
unnoticed...

---

# Libro y programa presence 2006

.left-column[
![Mackenzie book](data:image/png;base64,#img/mackenziebook.jpg)
]

.right-column[
![presence
software](http://www.mbr-pwrc.usgs.gov/software/doc/presence/falsePos.jpg)
]

Mackenzie populariza la ocupación `$(\psi)$` como un proxy de la abundancia teniendo en cuenta la detectabilidad `$(p)$`

---

# Libro y programa presence 2006

.left-column[
![Mackenzie book](img/mackenziebook2.jpg)
]

.right-column[
Una síntesis de enfoques basados en modelos para analizar datos de presencia-ausencia, considerando la detección imperfecta.
]

Mackenzie populariza la ocupación `$(\psi)$` como un proxy de la abundancia teniendo en cuenta la detectabilidad `$(p)$`

---

## Allows you to set goals and to monitor them over time.

![meta](data:image/png;base64,#img/meta.png)

---
class: inverse, middle, center

## Occupancy 
# `$$\psi$$`

## Detection probability

# `$$p$$`

### Occupancy is a reflection of other important population parameters such as density.

---

## 1.  `$(\psi)$` is the proportion of the sampled area that is occupied by the species.

## 2.  By visiting the site several times I can be more sure that I detect the species when it is found in that place.

## 3.  **Repeated sampling** are key.

## `$(\psi)$` It is influenced by environmental variables (**Covariables**) such as vegetation cover, altitude, precipitation, etc.

---

# This is what a data table with repeated sampling should look like

|      | visit1| visit2| visit3| visit4|
|:-----|------:|------:|------:|------:|
|site1 |      1|      0|      0|      1|
|site2 |      0|      0|      0|      0|
|site3 |      1|      1|      0|      0|
|sitex |      0|      0|      0|      0|

---

# Example calculating `$\psi$` and `$p$`

### Frequentist method (Maximum likelihood)

.pull-left[

|    | v 1| v 2| v 3| v 4|
|:---|---:|---:|---:|---:|
|s 1 |   1|   0|   0|   1|
|s 2 |   0|   0|   0|   0|
|s 3 |   1|   1|   0|   0|
|s x |   0|   0|   0|   0|
]

.pull-right[

| **Detection History**                  |
|----------------------------------------|
|  `$H_{1} \psi$` × p1(1-p2)(1-p3)p4             |
|  `$H_{2} \psi$` × (1-p2)(1-p2)(1-p3)(1-p4)p4 |
|  `$H_{3} \psi$` × p1p2(1-p3)(1-p4)             |
|  `$H_{4} \psi$` × (1-p2)(1-p2)(1-p3)(1-p4)p4 |

]

### Histories Combined in a Model:

$$
`\begin{aligned}
L(\psi, p \mid H_{1},...,H_{x}) =  \prod_{i=1}^{x} Pr (H_{i})
\end{aligned}`
$$
--

The model admits incorporating covariates to explain `$\psi$` and `$p$`

---

# Same example calculating `$\psi$` and `$p$`

### Bayesian method

.pull-left[

|    | v 1| v 2| v 3| v 4|
|:---|---:|---:|---:|---:|
|s 1 |   1|   0|   0|   1|
|s 2 |   0|   0|   0|   0|
|s 3 |   1|   1|   0|   0|
|s x |   0|   0|   0|   0|
]

.pull-right[

It is important to understand that there are two processes that can be modeled hierarchically

- The ecological process ($\psi$) follows a Bernoulli distribution.
- The observation model ($p$) follows a Bernoulli distribution.

The probability of observing the species given that it is present:

`$p = Pr(y_{i}=1 \mid z_{i}=1)$`

The Occupancy probability: `$\psi =Pr(z_{i}=1)$`

]

---

### A hierarchical (Bayesian) model

![Full Occu Bayes](data:image/png;base64,#img/Occu_Bayes.png)

### Admits Covariates

---

## Which one should I use? The maximum likelihood or Bayesian?

.pull-left[ 
ML

- Package [unmarked](https://cran.r-project.org/web/packages/unmarked/index.html)
- In R
- Admits "automatic" model selection AIC
- Problems with many NAs
- Hesian problem. estimates ok.
- Difficulty from 1 to 10: 3 if you already know R.

]

Bayesian

.pull-right[
- BUGS or Stan language, called from R
- Model selection is not that easy, BIC is not suitable 
- You don't have as many problems with many NAs in the matrix
- Estimates are more accurate.
- Difficulty from 1 to 10: 7 if you already know R.

]

---
class: middle, center

# Going Deep

![libro
azul](https://secure-ecsd.elsevier.com/covers/80/Tango2/large/9780123740977.jpg)

### Andy Royle (2008)

Advanced level book with lots of details, formulas, examples and code in R and BUGS language.

---

# Dragon-fly book (2015)

.pull-left[ 
![libro
libelula](https://images-na.ssl-images-amazon.com/images/I/513ulKHhAKL._SX404_BO1,204,203,200_.jpg)
]

.pull-right[ 
### More recent by [Marc Kery](http://store.elsevier.com/Marc-Kery/ELS_1059944/)

More than 700 pages clearly explaining where the theory comes from, in a tutorial style, starting with a basic level of R to advanced models and their implementation in R and the BUGS language.
]

---
background-image: url(data:image/png;base64,#img/baby-84626_1280.jpg)
background-size: contain

# Let's do it!

![Coding now](data:image/png;base64,#https://www.r-project.org/Rlogo.png) 
- R level? 
- Objects?, Vectors?
- DataFrame?
- Loops?
- Functions?

---

# Schedule

.left-column[
![Coding fast](data:image/png;base64,#http://i.giphy.com/fQZX2aoRC1Tqw.gif)
]

.right-column[

| Day       | Topic                                                                                                                                |
|-----------------|------------------------------------------------------|
| Tuesday 28 pm |  Remembering R                                                                                                                |
|           | [R as model tool](https://dlizcano.github.io/IntroOccuPresent/R_toModel_E.html)                                    |
| Wednesday 29 am | [Occupancy concept](https://dlizcano.github.io/IntroOccuPresent/modelOccuData_E.html)                        |
|           | Intro Occu Static model - [unmarked101](https://dlizcano.github.io/IntroOccuPresent/unmarked_101_E.html)                            |
| Wednesday 29 pm | Static Model in deep I- [Sim Machalilla](https://dlizcano.github.io/occu_book/)                                             |
|           | Static Model in deep II- [Data in unmarked](https://dlizcano.github.io/occu_book/unmarked.html) |
| Thursday 30 am | Questions. Real World Data - [Deer](https://github.com/dlizcano/Mazama_rufina)          |
|           | [More models](https://dlizcano.github.io/IntroOccuPresent/Otros_modelos_jerarquicos.html)                        |

]

---
class: bottom, center
background-image: url(data:image/png;base64,#img/children-593313_1280.jpg)
background-size: cover

# Thanks!

Slides created via the R package [**xaringan**](https://github.com/yihui/xaringan).

Contact: Diego J. Lizcano
<a href="http://twitter.com/dlizcano"> <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:steelblue;overflow:visible;position:relative;"><path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"/></svg>
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---

```r
xfun::session_info('rmarkdown')
```

```
## R version 4.2.2 (2022-10-31 ucrt)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 14393)
## 
## Locale:
##   LC_COLLATE=Spanish_Colombia.1252  LC_CTYPE=Spanish_Colombia.1252   
##   LC_MONETARY=Spanish_Colombia.1252 LC_NUMERIC=C                     
##   LC_TIME=Spanish_Colombia.1252    
## 
## Package version:
##   base64enc_0.1.3   bslib_0.4.2       cachem_1.0.7      cli_3.6.0        
##   digest_0.6.31     ellipsis_0.3.2    evaluate_0.20     fastmap_1.1.0    
##   fontawesome_0.5.0 fs_1.6.1          glue_1.6.2        graphics_4.2.2   
##   grDevices_4.2.2   highr_0.10        htmltools_0.5.4   jquerylib_0.1.4  
##   jsonlite_1.8.4    knitr_1.42        lifecycle_1.0.3   magrittr_2.0.3   
##   memoise_2.0.1     methods_4.2.2     mime_0.12         R6_2.5.1         
##   rappdirs_0.3.3    rlang_1.1.0       rmarkdown_2.21    sass_0.4.5       
##   stats_4.2.2       stringi_1.7.12    stringr_1.5.0     tinytex_0.44     
##   tools_4.2.2       utils_4.2.2       vctrs_0.5.2       xfun_0.37        
##   yaml_2.3.7       
## 
## Pandoc version: 2.19.2
```